Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
This article analyzes contests when contestants derive heterogeneous benefits from winning and investments are seen as costs to the contest designer. An example of this is sports leagues maximizing league profits. For sports leagues, optimal contests depend upon the heterogeneity of market sizes and the impact of team investment on winning. Sports leagues have mechanisms to change the structure of contests, implying they have some control of the expected payoff of teams, the value of the athletes, and the balance of the league. Data from Major League Baseball and the National Basketball Association are used to empirically estimate the model. (JEL C72, L10, L83)